Virginia SOL 4.MG.3.e
The Standard
Identify and represent rectangles with the same perimeter and different areas or with the same area and different perimeters.
Virginia Standards of Learning for Mathematics · The student will use multiple representations to develop and use formulas to solve problems, including those in context, involving area and perimeter limited to rectangles and squares (in both U.S. Customary and metric units).
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students draw or build rectangles that share a perimeter but have different areas. They also find rectangles that share an area but have different perimeters.
What Mastery Looks Like
- Students create and label rectangle dimensions that meet a given area or perimeter. They calculate both measures correctly and explain how the rectangles differ.
Common Misconceptions
- Students may think rectangles with equal perimeters must have equal areas. They may add side lengths for area, multiply for perimeter, or confuse units with square units.
How to Assess It
- Give students two tasks: draw two rectangles with perimeter 20 units and different areas, then draw two rectangles with area 24 square units and different perimeters.
Lesson moves
Ways to Teach It
Give pairs 24 square tiles and string, then have them build rectangles with equal areas and compare the string lengths around them.
Ask students to explain why a 1-by-12 rectangle and a 3-by-4 rectangle have equal areas but different perimeters.
Play a rectangle match game where students pair dimension cards that show equal areas or equal perimeters.
Plan two rectangular dog pens using 24 meters of fencing, then compare each pen's enclosed area.
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Printable 4.MG.3.e Worksheet
A ready-to-print activity worksheet aligned to 4.MG.3.e, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Related Standards
- 4.MG.3.f
Solve contextual problems involving area and perimeter of rectangles and squares.
- 4.MG.3.d
Use concrete materials and pictorial models to explore the relationship between area and perimeter of rectangles.
- 6.MG.2.b
Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.
- 4.MG.3.a
Use concrete materials and pictorial models to develop a formula for the area and perimeter of a rectangle (including a square).
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